LS factor: Length and slope factor in RUSLE

LS factor: Length and slope factor in RUSLE

What is LS-Factor??

If we study soil loss in a river basin or in a particular area, then we summaries the several factor that are participating in soil erosion or indirectly hit the erosion activity in that area.
Among them most important factor is the topography which directly hit the erosion process in the area. The influence of topography in soil erosion can be assess using the topographic factor (LS factor) which is used in RUSLE model to calculate the soil erosion in a river basin. It contains simply two component as slope length factor (L-factor) and slope steepness actor (S-factor). This means length and steepness (gradient) of slope affect the soil erosion in a river basin and as length and steepness will increase, it lead to increase in erosion in that area.  Before studying the influence of L-factor in soil erosion, it is necessary to know L-factor.

What is Slope length factor (L-factor)??

The L-factor (Wischmeier and Smith 1978) is ratio of soil loss due to slope length of a region to soil loss from a region that has a slope length of 22.1m. Here 22.13 is

the slope length of the area on which RUSLE model was tested.

 L-factor = (λ/22.13) m

Where λ is slope length of the area for which L-factor is calculated and 22.13 is RUSLE unit plot length in meter in which experiment was performed to evaluate the formula of L-factor.

And m is variable of slope length exponent which varies from 0.2 to 0.5 depending of the slope percentage (Wischmeier and Smith 1978).

What is slope length??

The slope length (λ) is length between two point from where the overland flow started and to where the river start deposition or to where runoff joins to well define channel.
The deposition in river may be due to several causes and one of these is decreasing of slope. As the slope length increase, the soil erosion will also increase as high water overflow in downslope portion.

What is Slope steepness/ gradient factor (S-factor)??

S-factor show the roll of steepness on soil loss and this factor more influence the soil erosion than the L-factor as more the steepness and more the soil loss in the basin. Ongoing increasing the slope steepness the flow velocity of river water will increase which will allow to increase the erosion activity in the area.
The L-factor and S-factor together represent the LS-factor which contribute erodibility due to combine action of slope length and steepness.

How to calculate LS –factor for river basin??

There are various method are available for calculation LS factor using the GIS environment.
Data required: Dem (Digital elevation model)

GIS platform: Arc-GIS/Q-GIS/SAGA-GIS

Methods to calculate the LS factor

• Using Wis­chmeier and Smith (1978) formula

LS = (λ/22.13)^m × (65.4sin2β + 4.5sinβ + 0.0654)
Here
L-factor= (λ/22.13)^m  and
S-factor = (65.4sin2β + 4.5sinβ + 0.0654)
λ= Slope length in meter (λ= flow accumulation*cell size)
β= Slope angle in radian
m = 0.5 if β > 0.05
m = 0.4 if 0.03 < β > 0.05
m = 0.3 if 0.01 < β > 0.03
m = 0.2 if β < 0.01

• Using Moore and Burch (1986) and Moore and Wilson (1992)

LS = (As/22.13)^0.4 × (sinβ/0.0896)^1.3
Here
L-factor = (As/22.13)^0.4
S-factor= (sinβ/0.0896)^1.3
As= specific catchment area
β= Slope angle in radian

• Steepness factor by Liu et al. (1994) and Liu (2002)
  

S= 10.80*sinƟ+0.03 if Ɵ < 0.5
S =16.80*sinƟ-0.5 if 5< Ɵ<10
S=21.91*sinƟ-0.96 if Ɵ>10
Ɵ is the slope gradient in degree.

These methods are available on the SAGA-GIS and Q-GIS environment from which we can calculate the LS-factor directly using DEM data.